Method and apparatus for plasma processing

ABSTRACT

The invention provides a plasma processing apparatus capable of minimizing the non-uniformity of potential distribution around wafer circumference, and providing a uniform process across the wafer surface. The apparatus is equipped with a focus ring formed of a dielectric, a conductor or a semiconductor and having RF applied thereto, the design of which is optimized for processing based on a design technique clarifying physical conditions for flattening a sheath-plasma interface above a wafer and the sheath-plasma interface above the focus ring. A surface voltage of the focus ring is determined to be not less than a minimum voltage for preventing reaction products caused by wafer processing from depositing thereon. The surface height, surface voltage, material and structure of the focus ring are optimized so that the height of an ion sheath formed on the focus ring surface is either equal or has a height difference within an appropriate tolerance range to the height of the ion sheath formed on the wafer surface. Optimization of the structure is realized by setting up an appropriate tolerance range taking into consideration the variation caused by consumption of the focus ring.

The present application is based on and claims priority of Japanesepatent application No. 2004-118513 filed on Apr. 14, 2004, the entirecontents of which are hereby incorporated by reference.

FIELD OF THE INVENTION

The present invention relates to the art of semiconductor fabrication.Especially, the invention relates to a structure of a wafer stage thataffects the etching contour when providing an etching process to asemiconductor wafer using plasma.

DESCRIPTION OF THE RELATED ART

Recently, along with the enhancement in the integration of semiconductorelements, the circuit patterns have become more and more refined, andthe demanded accuracy of processing dimension has become stricter.Further, the wafer diameter is increased to 300 mm in the attempt toreduce fabrication costs of the semiconductor elements, but processingis required to be uniform across the whole surface of the wafer from thecenter to the outer circumference thereof. However, a ceramic cover forprotecting an electrostatic chuck is disposed near the outercircumference of the wafer, for example, which causes non-uniformity ofthe electric field at the circumference compared to the center of thewafer, and causes the drawback of non-uniformity of the wafer process.If electric field non-uniformity is caused near the outer circumferenceof the wafer, the ions being incident on the wafer will not beperpendicular to the wafer, by which the perpendicularity of the contouris deteriorated and the yield factor reduced. Similarly, focusing anddivergence of the ions occur, by which the processing performance suchas the etching rate varies greatly near the wafer edge. These areserious problems since they cause the increase of fabrication costs.

In order to solve this problem, many measures have been proposed forpreventing the distortion of electric field of the electrode on whichthe wafer is placed. The structure for realizing this is called a focusring or an edge ring, and in this specification it is referred to as afocus ring. For example, a dry etching device equipped with a ring typeauxiliary plate having an adjustable height for surrounding theperiphery of the wafer is proposed (refer for example to patent document1). Further, a means for controlling an RF power (voltage or electricfield) applied to the wafer edge and the outer periphery thereof bycontrolling the impedance of the wafer edge and the outer peripherythereof is proposed (refer for example to patent document 2). Similarly,structures for controlling the electric field near the wafer edge with afocus ring having RF applied thereto are proposed, wherein the focusring is a conductive member (refer for example to patent document 3) orwherein the focus ring is a dielectric (refer for example to patentdocument 4). Further, there is a proposal of an elevated focus ring(edge ring) formed of a dielectric material or a semiconductor materialfor flattening the sheath-plasma interface above the wafer and thesheath-plasma interface above the focus ring when RF is not applied, anda focus ring (edge ring) having the same height as the wafer formed ofdielectric or semiconductor material for flattening the sheath-plasmainterface above the wafer and the sheath-plasma interface above thefocus ring when RF is applied thereto (refer for example to patentdocument 5). Moreover, there is a proposal of a focus ring formed byassembling a dielectric and a conductor for generating a uniform sheathvoltage by making the impedance between the lower electrode and plasmaequal at both the wafer and the focus ring (refer for example to patentdocument 6).

Moreover, a method for achieving a uniform process is proposed, thatadjusts the intensity of RF passing the focus ring by adjusting theimpedance thereof (refer for example to patent document 7). Moreover,another method for achieving a uniform process through use of a focusring having the same height as the wafer surface is proposed (refer forexample to patent document 8).

Patent Document 1:

Japanese Patent Application Laid-Open No. 63-229719

Patent Document 2:

Japanese Patent Application Laid-Open No. 6-120140

Patent Document 3:

Japanese Patent Application Laid-Open No. 5-335283

Patent Document 4:

Japanese Patent Application Laid-Open No. 6-168911

Patent Document 5:

International Publication under PCT No. WO 01/01445 A1 (Published inJapan as P2003-503841)

Patent Document 6:

International Publication under PCT No. WO 01/50497 A1 (Published inJapan as P2003-519907)

Patent Document 7:

Japanese Patent Application Laid-Open No. 2002-198355

Patent Document 8:

Japanese Patent Application Laid-Open No. 2003-229408

Patent Document 9:

Japanese Patent Application Laid-Open No. 2002-203835

According to the above-mentioned prior art methods, however, there is nodisclosure of a technique for optimizing the focus ring structure. Evenif the focus ring structure is determined through experiments, thedesign of the focus ring must be reconsidered each time the etchingprocess is changed. In a general fabrication process, a single apparatusis not only used to carry out a single discharge process, but used tocarry out multiple discharge conditions. Therefore, the focus ring mustbe exchanged depending on discharge conditions. In an alternativetechnique, a single focus ring structure can be designed to correspondto various discharge conditions by setting up a tolerance and optimizingthe structure corresponding to the set tolerance. However, the prior artlacks to disclose such technique.

Furthermore, since the focus ring is subjected to the application of RFvoltage while being exposed to reactive plasma, the ring is consumedboth physically by ions (through sputtering etc.) and chemically byreaction, by which the dimension of the ring is changed. Therefore, theelectric field correcting function of the focus ring changes with timeand deteriorated. Therefore, it is necessary to set up a tolerance andto optimize the structure accordingly, but the prior art lacks todisclose such technique.

On the other hand, reaction products generated through wafer processingand reaction products in the gas may be deposited on the surface of thefocus ring, depending on the property of the wafer processing. Thedeposits on the focus ring surface may become particles that adhere tothe wafer and cause defective products to be fabricated. Further, duringthe course of the procedure starting from the state in which there areno deposits to the state in which sufficient deposition is formed, thegas-phase components released from the focus ring surface are varied,according to which the plasma status is changed. This may cause timevariation of the wafer process according to which the result of waferprocessing is changed with time from the starting of wafer processing.The conventional methods lack to provide a method for coping with thedeposition, so the focus ring may be helpful to uniformize theprocessing, but it is not actually useful if deposition occurs.

As disclosed in patent document 5 mentioned above, in order touniformize the process at the wafer edge portion, it is important thatthe plasma-sheath interface above the wafer and the plasma-sheathinterface above the focus ring are flat. However, the ion trajectorytoward the wafer does not depend only on the plasma-sheath interface,but also on the flatness of the potential field within the sheath. Thelatter important factor has not been considered in the conventionalattempt to optimize the structure. Of course, patent document 5 lacks todisclose any teachings related to determining the tolerance andoptimizing the structure based thereon. The drawback of the conventionaloptimization process disclosed in document 5 is that there is noteaching of a physical method or design technique for flattening theplasma-sheath interface above the wafer and the plasma-sheath interfaceabove the focus ring. The optimization of the structure is impossible tocarry out without a physical mechanism or a design technique. Even whenan appropriate structure is discovered through experimental methods, itis difficult to prove experimentally that the plasma-sheath interfaceabove the wafer and the plasma-sheath interface above the focus ring areflat, and the flatness cannot be ensured.

The drawback of the technique disclosed in patent document 6 mentionedabove is that the generation of a uniform sheath voltage realized byequalizing the impedance between the lower electrode and plasma at thewafer portion and at the focus ring portion does not guarantee theflattening of the plasma-sheath interface above the wafer and theplasma-sheath interface above the focus ring. An additional conditionmust be fulfilled to ensure that the plasma-sheath interface above thewafer and the plasma-sheath interface above the focus ring are flat, butpatent document 6 lacks to teach such condition.

A more detailed description of these drawbacks will appear in thedescription of the preferred embodiment of the present invention.

Considering the above drawbacks of the prior art, the first object ofthe present invention is to provide a wafer processing method and anetching apparatus comprising a wafer stage capable of providing uniformprocessing across the whole wafer plane, while minimizing thenon-uniformity of the potential distribution around the wafercircumference.

The second object of the present invention is to provide a waferprocessing method and an etching apparatus comprising a wafer stage,wherein a tolerance of the wafer stage has been set up and the structureof the wafer stage is optimized to correspond to the set tolerance, inorder to provide uniform processing across the wafer plane.

SUMMARY OF THE INVENTION

The first object of the present invention is achieved by providing afocus ring made of a dielectric, a conductor or a semiconductor, andhaving RF applied thereto. However, at this time, the surface voltage ofthe focus ring must be not less than a minimum voltage for preventingreaction products generated by the wafer processing from depositingthereon. The present invention is also characterized in that the surfaceheight, the surface voltage, the material and the structure of the focusring are optimized so that the height of the ion sheath formed on thefocus ring surface is either equal or has a height difference within anappropriate tolerance range to the height of the ion sheath formed onthe wafer surface. Furthermore, the present invention characterizes inthat the optimization of structure is performed based on a tolerance setappropriately by taking into consideration the variation by time of thefocus ring caused by consumption.

The first and second objects of the present invention are achieved byclarifying the physical conditions for flattening the plasma-sheathinterface above the wafer and the plasma-sheath interface above thefocus ring, and by establishing a design technique for designing theactual structure thereof.

More specifically, the present invention provides a plasma processingapparatus for processing an object to be processed using plasma and amethod for plasma processing using this apparatus, the apparatuscomprising a process stage for placing the object to be processed; and afocus ring disposed on the process stage surrounding the object to beprocessed, the focus ring and the object to be processed being subjectedto application of RF bias; wherein a structure of the focus ring and theprocess stage is optimized through an optimization design technique byequivalent circuit analysis.

According to the plasma processing apparatus or plasma processing methodmentioned above, the optimization design technique includes anequivalent circuit modeling of plasma and ion sheath based on aplasma-sheath model; or the optimization design technique optimizes afocus ring surface potential so as to prevent wafer process reactionproducts from adhering to the focus ring; or the optimization designtechnique optimizes a focus ring surface height, a focus ring surfacevoltage, a focus ring material and a focus ring structure so that aheight of an ion sheath formed on the focus ring surface is either equalor has a height difference within an appropriate tolerance range to aheight of an ion sheath formed on the wafer surface; or the optimizationdesign technique optimizes the structure by setting up an appropriatetolerance taking into consideration a variation by time caused byconsumption of the focus ring; or the optimization design technique aimsat flattening as much as possible an equi-potential surface within anion sheath through the equivalent circuit analysis and, when necessary,a sequential coupling analysis based on two dimensional plasma analysisand two dimensional electric field analysis.

Furthermore, according to the plasma processing apparatus and plasmaprocessing method mentioned above, the optimization design techniquecomprises two plasma-sheath interface flattening conditions, one ofwhich is that a voltage drop of an RF voltage from an electrode in theprocess stage to the plasma-sheath interface above the object to beprocessed must be equal to the voltage drop of the RF voltage from theelectrode in the processing stage to the plasma-sheath interface abovethe focus ring; and the other plasma-sheath interface flatteningcondition is that a sum of a surface height of the object to beprocessed measured from a certain height reference point and a sheaththickness above the object to be processed must be equal to a sum of asurface height of the focus ring measured from the height referencepoint and the sheath thickness above the focus ring.

Further, the present invention provides a focus ring of a plasmaprocessing apparatus for processing an object to be processed usingplasma, the apparatus comprising a process stage for placing the objectto be processed, and the focus ring disposed on the process stagesurrounding the object to be processed, the focus ring and the object tobe processed being subjected to application of RF bias; wherein thematerial of the focus ring has a relative dielectric constant of 10 orless.

Moreover, the present invention provides a focus ring of a plasmaprocessing apparatus for processing an object to be processed usingplasma, the apparatus comprising a process stage for placing the objectto be processed, and the focus ring disposed on the process stagesurrounding the object to be processed, the focus ring and the object tobe processed being subjected to application of RF bias; wherein thefocus ring comprises a first focus ring formed of a dielectric materialhaving a relative dielectric constant of 10 or less, and a second focusring formed to surround the first focus ring.

As mentioned, according to the present invention, the focus ringstructure can be optimized to correspond to the object of waferprocessing through use of an equivalent circuit analysis, a twodimensional plasma analysis, a two dimensional electric field analysisand plasma-sheath interface flattening conditions, and through use ofthe optimized structure, can maximize the uniformity of the process rateand processed structure shape across the whole wafer surface.

Furthermore, the present invention enables to prevent deposition ofprocess reaction products on the focus ring surface, by which the lifeof the focus ring can be extended significantly.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic cross-sectional view showing the overall structureof a plasma processing apparatus according to the present invention;

FIG. 2 is a graph showing the relationship between RF potential, plasmaspace potential and sheath voltage;

FIG. 3 is an enlarged cross-sectional view near a focus ring of a plasmaprocessing apparatus corresponding to a first embodiment of the presentinvention;

FIG. 4 shows the most simplified equivalent circuit corresponding to thefirst embodiment of the present invention;

FIG. 5 is a graph showing an example for seeking a true ion saturationcurrent by experiments;

FIG. 6 is an equivalent circuit diagram of ion sheath and plasma;

FIG. 7 is a flowchart showing an equivalent circuit analysis method;

FIG. 8 is a modified equivalent circuit diagram for deriving aplasma-sheath interface flattening condition;

FIG. 9 is an enlarged cross-sectional view showing the area near thefocus ring of the plasma processing apparatus corresponding to a secondembodiment of the invention;

FIG. 10 is a graph showing the relationship between a tolerance ofprocess variation and a tolerance of sheath height difference;

FIG. 11 shows a third embodiment of the present invention, wherein (a)shows a final focus ring structure taking into consideration a toleranceof process variation, and (b) shows a focus ring structure at the end ofits life, having designed to take into consideration the tolerance ofprocess variation;

FIG. 12 is a graph showing the relationship between the focus ringsurface voltage and the focus ring etch or the deposition of processreaction products on the focus ring;

FIG. 13 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a fourthembodiment of the present invention;

FIG. 14 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a fifthembodiment of the present invention;

FIG. 15 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a sixthembodiment of the present invention;

FIG. 16 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a seventhembodiment of the present invention;

FIG. 17 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to an eighthembodiment of the present invention;

FIG. 18 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a ninthembodiment of the present invention;

FIG. 19 is a graph showing a relative dielectric constant dependency ofthe relationship between focus ring consumption and sheath heightdifference;

FIG. 20 is an enlarged cross-sectional view showing the area near afocus ring of a plasma processing apparatus corresponding to a tenthembodiment of the present invention; and

FIG. 21 is an equivalent circuit diagram corresponding to the tenthembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The overall structure of a plasma processing apparatus according to thepresent invention will now be described with reference to the schematiccross-sectional view of FIG. 1. The plasma processing apparatuscomprises a processing chamber 1 formed of conductive material such asaluminum, and an antenna 2 and a shower plate 3 are attached to theinterior of the chamber via respective support flanges 5 and 6. Gas issupplied between the antenna 2 and the shower plate 3 via a process gasinlet pipe 7 from the atmosphere, and showered into the processingchamber 1 through multiple micropores formed to the shower plate 3. Theantenna 2 is formed of a conductor, but the shower plate 3 can be formedof a conductor, a dielectric or a semiconductor. If the shower plate 3is formed of conductive material or semiconductor, the shower plate 3acts as an antenna for transmitting electric power directly to plasma.The process gas is evacuated via an evacuation duct 10 into an evacuator11, so that the chamber is maintained at a pressure suitable forprocessing. By supplying through a first RF power supply 4 a radiofrequency of a predetermined frequency and power, plasma 9 is generatedwith parameters preferable for processing. A magnet (electromagnet) 8can be used to control the plasma parameters, but can be omitted. Theconfiguration mentioned here relates to a discharge method so-called acapacitive coupled discharge, but according to the present invention,other types of discharge methods such as electron cyclotron resonancedischarge and inductive coupled discharge can also be adopted as long asplasma having appropriate properties for processing is generated. Ofcourse, the configuration of the discharge unit should correspond to thedischarge method being adopted, and should not be restricted to the onedescribed here.

A wafer (substrate to be processed) 12 is carried into the processingchamber 1 through a gate (not shown) from the atmosphere, and placed onan electrode 14 by an appropriate transfer device (not shown). The upperface of the electrode 14 is provided with an electrostatic chucking film(not shown) with appropriate property to chuck the wafer by the voltageapplied thereto via a chalk coil 22 from a DC power supply 23 disposedoutside. The electrode 14 further has a refrigerant channel 15 formed tothe interior thereof, to which refrigerant is supplied from the outside(not shown), so as to control the temperature of the wafer 12 to atemperature appropriate for processing. A focus ring 13 is disposed tothe outer circumference area of the wafer 12, and a susceptor 16 isdisposed to protect the electrode 14 from plasma 9. The electrode 14 isattached to the processing chamber 1 via an insulating base 17 and anelectrode base flange 18. The electrode 14 can be moved up and down viaan appropriate elevation mechanism (not shown), when it is desirable tovary the distance between the wafer 12 and the shower plate 3. Thepresent invention can be applied regardless of whether such elevationmechanism is adopted. An RF power is supplied from a second RF powersupply 21 via a blocking capacitor 20 and a conductor protected by aninsulating duct 19 to the electrode 14, according to which an RF bias isapplied to the wafer 12. As mentioned, the first RF power supply 4 isnot necessary configured as illustrated, and for example, the outputthereof can be applied to the blocking capacitor 20 in parallel with thesecond RF power supply 21. It is also possible to omit the fist RF powersupply 4, and to have the second RF power supply 21 work both togenerate plasma 9 and to apply RF bias to the wafer 12.

Next, FIGS. 2 through 8 are referred to in describing how the RF bias isapplied to the wafer and focus ring, how the thickness of the ion sheathrelates to this phenomenon, and how the focus ring is designed based onan equivalent circuit model corresponding to these physical phenomena.The applications of RF bias to the wafer surface and to the focus ringsurface are the same phenomena, so we will only describe the applicationto the wafer. FIG. 2 shows the relationship between the RF potentialwaveform on the wafer surface (V_(w)) and the plasma space potential(V_(s)). The peak-to-peak voltage V_(pp) of the RF potential waveformand the self-bias voltage V_(dc) are defined in the drawing. Theself-bias voltage V_(dc) is a potential in which the sum of electroncurrent and ion current flowing into the wafer from plasma is net zerofor one RF cycle, and it is also the time-average value of the surfacevoltage of wafer. On the other hand, the plasma space potential takes afixed value when RF voltage is sufficiently low (defined as V_(s0) inFIG. 2), but when the RF potential exceeds the plasma space potential,it increases along with RF potential, and substantially equals RFpotential when the RF potential takes the maximum value. The reason whythe plasma space potential increases along with the RF potential is thatthe plasma becomes ion rich since the increasing RF potential draws outa large amount of electrons from plasma. Now, the ratio of V_(dc) andV_(pp) (V_(dc)/V_(pp)) depends on the RF frequency and the groundimpedance seen from the wafer, and if the energy distribution functionof electrons in the plasma corresponds to a Maxwell distribution, it isalways 0<V_(dc)/V_(pp)<0.5. As the RF frequency increases, and as theimpedance of the ground increases, V_(dc)/V_(pp) approximates 0. Inother words, V_(dc)/V_(pp) is a value specific to the apparatus, and thedesigner of the apparatus can acquire the value easily throughmeasurement, or through analysis (simulation) of related experimentaldata. Once this value is acquired, the value of V_(dc) can be computedeasily by measuring V_(pp) (or by calculating the same by circuitsimulation). Here, based on FIG. 2, the voltage V_(sh)(t) applied to theion sheath formed on the wafer surface varies with time t, and can beexpressed by the following formula.

[Formula 1]V _(sh)(t)=V _(s)(t)−V _(w)(t)  (1)

Next, sheath thickness will be described. Sheath thickness can beexpressed by a function of Debye length λ_(d) and sheath voltage,regardless of whether the sheath is DC sheath or RF sheath. This isbecause Debye length is the unit length of electric field shielding bycharged particles, so whether the sheath voltage can be maintained(wafer voltage can be shield) or not is determined by forming a sheaththickness that corresponds to how many times the Debye length. Whetherto treat the sheath as a matrix sheath or a Child-law sheath, or whetherto consider the effect of collision, are determined by the operationstatus of the apparatus. Here, we will describe the case where Child-lawsheath is used as an example. As can be seen from FIG. 2, since thesheath voltage varies within one RF cycle, the sheath thickness is alsovaried within one RF cycle. However, in order to compute the surfacevoltage of the focus ring or wafer using the equivalent circuit modeldescribed later, the variation in sheath thickness (as illustrated inFIG. 3, sheath thickness is an important element for determining thesheath impedance) makes handling difficult. Therefore, we will consideraveraging the sheath thickness (impedance) within a single RF cycle. Inthis case, the average d_(sh) of sheath thickness can be calculatedusing the following formula.

[Formula 2]

$\begin{matrix}{d_{sh} = {0.642\frac{\lambda_{d}}{\tau}{\int_{0}^{\tau}{\left( \frac{2{V_{sh}(t)}}{T_{e}} \right)^{\frac{3}{4}}\ {\mathbb{d}t}}}}} & (2)\end{matrix}$

-   -   wherein t represents time of a single Rf cycle, and Te        represents electron temperature.

The important thing is to acquire a tool for designing the focus ring bydefining the relationship between the wafer surface voltage and sheaththickness, and what type of formula is used to compute the voltage andsheath thickness is not important. The formula to be used for thepresent invention can be made more simplified or more complex, as longas the design accuracy can be ensured as a result.

We will now describe the method of replacing the above-mentioned theorywith a specific equivalent circuit model. For simplicity, a structureillustrated in FIG. 3 showing a first embodiment of the presentinvention will be considered. On the surface of an electrode 33, adielectric film 34 for electrostatic chucking is formed via thermalspray coating of alumina or the like. A wafer 30 and a focus ring 31 aremounted thereon, and a susceptor 32 for protecting the electrode 33 anddielectric film 34 is disposed. Although not shown, an RF power supplyand a DC power supply for electrostatic chucking are connected to theelectrode 33, by which the wafer 30 is chucked to the dielectric film34, and the wafer 30 and focus ring 31 are subjected to RF bias.

Plasma region 37 is formed above the wafer 30 and focus ring 31, and anion sheath region 36 is formed below a plasma-sheath interface 35. Now,the sheath thickness d_(sh) given in formula 2 is the distance betweenthe surface of wafer 30 (or focus ring 31) and plasma-sheath interface35, and corresponds to d_(w) or d_(FR) in FIG. 3. In general, the wafer30 can be handled as a conductor. That is, even if a dielectric film isformed on the wafer surface, the thickness thereof is very thin, so thecapacitance of the wafer is greater by few digits than the capacitanceof the dielectric film 34. Therefore, the impedance thereof is smallerby few digits, and it will not affect the overall circuit operation. Ifthis precondition is not true, one should simply substitute the waferwith a more detailed equivalent circuit and determine the circuitconstant thereof. The most direct method is to use a network analyzer todirectly measure the impedance from the electrode 33 to the wafer 30surface. According to this method, it is possible to obtain theimpedance value for substitution to a simple equivalent circuit withouthaving to determine a complex equivalent circuit and its circuitconstant. By carrying out this measurement for a few structures, it ispossible to determine the impedance through interpolation/extrapolationeven when the structure is changed.

The material of the focus ring 31 can be a dielectric, an insulator, asemiconductor or a combination thereof. It is also possible to computethe equivalent circuit using the material property and shape regardingthe focus ring.

Further, it is also possible to calculate the impedance of a necessarysection directly using the aforementioned network analyzer. According toone example, the capacitance between the electrode 33 and the Si focusring 31 is calculated to be 4467 pF. On the other hand, the capacitancecomputed from the impedance measured by the network analyzer is 4513 pF,which showed a favorable match. Regardless of the shape, structure andproperty of the wafer 30 and focus ring 31, the RF power applied to theelectrode 33 passes through the surface of the wafer 30 and focus ring31 and is transmitted to the sheath 36 and plasma 37, so it isrealistically possible to compute the impedance thereof. If the focusring 31 is a dielectric or a semiconductor, it is possible to measurethe impedance by forming an electrode to the necessary portion (forexample, by depositing aluminum or copper film). Whether or not toincorporate the susceptor 32 to the equivalent circuit should bedetermined based on whether the impedance between the electrode 33 andsusceptor 32 surface is negligible compared to the impedance between thewafer 30 or focus ring 31.

The circuit illustrated in FIG. 4 is one example of the most simplifiedequivalent circuit corresponding to FIG. 3. Here, the RF power supply 40is connected to the electrode 33. Power is supplied from the electrode33 to the wafer surface 43 (wafer 30) via a capacitor 42 (C1)representing the electrostatic chucking dielectric film 34 formed on theelectrode 33. The impedance 44 (Z_(W)) to the ground via the ion sheath36 and plasma 37 seen from the wafer surface 43 can be expressed asZ_(W)=R_(W)+jX_(W) for any impedance. Here, R_(W) represents resistancecomponent, j represents imaginary unit (j²=−1), and X_(W) representsreactance (generic term for inductance and capacitance) component.Similarly, power to the focus ring 31 is supplied from the electrode 33to the focus ring surface 47 via a capacitor 45 (C2) representing thedielectric film 34. The example of FIG. 4 corresponds to the case inwhich the focus ring is formed of a dielectric, and power is transmittedto the focus ring surface 47 via a capacitor 46 (C3) representing thedielectric focus ring 31. The load impedance 48 (Z_(F)) seen from thefocus ring surface 47 can be expressed as Z_(F)=R_(F)+jX_(F), similar tothe case of the load impedance 44 (Z_(W)) seen from the wafer surface43.

Here, R_(F) represents resistance component, and X_(F) representsreactance component. However, the equivalent circuit shown in FIG. 4 isa mere example, and it should be noted that any type of structure can bereplaced with an equivalent circuit. The equivalent circuit is not onlyrestricted to the simple one illustrated here, but can be replaced withamore complex circuit, such as two-dimensional or three-dimensionalequivalent circuits. For any material and structure, the elements of thecircuit are limited to a capacitor, a coil and a resistance, so thenumerical analysis of the circuit is easy. The complexity of theequivalent circuit should be determined according to the necessarydesign accuracy. The aforementioned direct measurement using the networkanalyzer is very effective, since it is highly accurate and simplifiesthe equivalent circuit.

In FIG. 4, the current (I_(W)) seen from the surface voltage of thewafer surface 43 can be expressed as I_(W)=A+jB (A), as illustrated inFIG. 4. The real part A of this current is known to correspond to theion saturation current flowing into the wafer surface 43. The method fordetermining the electron density and electron temperature of plasmausing this ion saturation current component has already been taught(refer for example to patent document 9). Thus, the designer candetermine the plasma parameters with high accuracy by carrying outexperiments and analysis regarding the process for optimizing focus ringstructure.

FIG. 5 is an example of an experiment carried out to obtain the true ionsaturation current (ICF) and the result of analyzing the same. When theelectron temperature and electron density are achieved, the Debye lengthλ_(d) of formula 2 can be computed easily based on the following formula3, according to which formula 2 can be calculated.

[Formula 3]

$\begin{matrix}{\lambda_{d} = \sqrt{\frac{ɛ_{0}T_{e}}{e\; n_{0}}}} & (3)\end{matrix}$

-   -   wherein e₀ represents the dielectric constant in vacuum, e        represents elementary charge, and n₀ represents electron        density.

Next, we will explain the method for determining the equivalent circuitof plasma and sheath and the impedance thereof. Note that by using themethod disclosed in patent document 9, the designer can determine thetotal impedance of plasma and sheath without having to assemble acomplex equivalent circuit or perform calculation. Through analysis of afew appropriate experimental data and creating a database based thereon,the designer can determine the necessary impedance by interpolation orextrapolation. It is important to handle plasma as an equivalentcircuit, and it is not important what type of equivalent circuit isassembled. It is necessary to simply assemble an equivalent circuit thatfulfills the necessary accuracy as a result.

Now, we will describe a simplified plasma-sheath equivalent circuitshown in FIG. 6. The load impedance seen from wafer (focus ring) surface50 can be represented by connecting in series a parallel connection ofthe resistance component (R1) 52 of the ion sheath on the wafer (focusring) surface and the condenser component (C4) 51, the impedancecomponent (Zp) 53 of plasma, and a parallel connection of the resistancecomponent (R2) 55 of the ion sheath on the ground surface and thecapacitance component (C5) 54. Moreover, it is possible to represent thesheath resistance component with a diode, and it is possible toincorporate the plasma resistance, plasma capacitance and plasmainductance. As mentioned, it is important to form the equivalentcircuit, but the type of the equivalent circuit being formed is notimportant as long as desired accuracy is achieved.

Using formula 2, the condenser component (C4) 51 on the wafer (focusring) surface calculates the sheath thickness d_(sh). The sheath voltageV_(sh) is set to an appropriate assumed value, and the solution iscomputed by a convergent calculation mentioned later. When the sheaththickness is calculated, the capacitance C_(sh) of the sheath can becomputed easily based on the following formula 4.

[Formula 4]

$\begin{matrix}{C_{s\; h} = \frac{ɛ_{0}S_{s\; h}}{d_{s\; h}}} & (4)\end{matrix}$

-   -   wherein S_(sh) represents the (wafer, focus ring) surface area        of the sheath.

Next, regarding the resistance component (R1) 52 of the ion sheath onthe wafer (focus ring) surface, it can be expressed by the followingformula 5 by simply assuming that the ion saturation current flows by anaverage sheath voltage. ICF is the true ion saturation currentcalculated in FIG. 5.

[Formula 5]

$\begin{matrix}{R = \frac{I\; C\; F}{\frac{1}{\tau}{\int_{0}^{\tau}{{V_{s\; h}(t)}\ {\mathbb{d}x}}}}} & (5)\end{matrix}$

Further, the behavior of the electron current and ion current flowinginto the wafer and focus ring is similar to the case of a double probe,so it is possible to use the theoretical formula for the double probe.According to the experience of the inventors, the double probe theory ismore accurate. Further, it is also possible to use a single probetheory, but the result is not so different. The resistance component(R2) 55 of the ion sheath on the ground surface and the capacitancecomponent (C5) 54 are also calculated by initially providing anappropriate voltage to the convergent calculation. Whether or not theplasma impedance (Zp) 53 should be evaluated depends on the RF frequencybeing used. If it is sufficiently smaller than the sheath impedance, itis negligible. The total impedance of the equivalent circuit of FIG. 6mentioned above becomes the wafer load impedance 44 or the focus ringload impedance 48 of FIG. 4. Based on the described method, theequivalent circuit of FIG. 4 is completely capable of numericalanalysis.

The steps of equivalent circuit analysis are described in FIG. 7. Here,the plasma parameters and sheath voltage given as initial conditions aresubjected to convergent calculation. That is, the necessary plasmaparameters, RF power and sheath voltage are provided as initialconditions (S1). Next, the impedance of the equivalent circuit iscalculated (S2). Using the acquired impedance, the voltage and currentof each part of the equivalent circuit are calculated, and based onthese values, the plasma parameters and sheath voltage are calculated(S3). It is then determined whether the plasma parameters and sheathvoltage provided in step S1 are equal to the plasma parameters andsheath voltage acquired by the calculation of step S3 (S4), and if theyare not equal, the calculated plasma parameters and sheath voltage areprovided (S5), and the procedure returns to step S2 where the impedanceof the equivalent circuit is calculated using the calculated results.When in step S4 the given plasma parameters and sheath voltage areequal, the equivalent circuit analysis procedure is completed, and theconvergent calculation is simply converged. As a result, the voltage onthe surface of the wafer and focus ring and the sheath height thereofcan be acquired.

If it is considered that the conditions for matching the sheath heighton the focus ring and sheath height on the wafer are the most suitableconditions, it is sufficient to use the present equivalent circuitanalysis. However, ion trajectory of the ions incident from the plasmadepend not completely on the plasma-sheath interface conditions, butalso on the electric field within the sheath. Therefore, in order toclarify the ion trajectory, it is necessary to perform sequentialcoupled analysis in the following order: two-dimensional plasma analysis(S10) and two-dimensional electric field analysis (S20) based on theresult of the aforementioned equivalent circuit analysis. If necessary,interactive sequential coupled analysis can be performed between thetwo-dimensional plasma analysis and two-dimensional electric fieldanalysis. Thereby, the electric field structure around the wafer andfocus ring, including the electric field in the dielectric, can bedetermined. The codes for performing two-dimensional plasma analysis andtwo-dimensional electric field analysis are commercially available, andwill not be described here.

Now, we will describe the conditions for flattening the plasma-sheathinterface on the wafer surface and the plasma-sheath interface on thefocus ring surface, or in other words, the plasma-sheath interfaceflattening conditions. The first one is described with reference to FIG.8, which is a rewritten view of FIG. 4 in which the equivalent circuitis illustrated in a more understandable way. There are two routesthrough which power is transmitted from the electrode 33 connected tothe RF power supply 40. The first route passes impedance 60 (Z_(F1))between the electrode 33 (voltage V₀) and focus ring surface 47 (voltageV_(F1)), impedance 61 (Z_(F2)) between the focus ring surface 47 andplasma-sheath interface 62 (voltage V_(F2)) on the focus ring, impedance63 (Z_(F3)) between plasma and ground, and reaches the ground. Thesecond route passes impedance 64 (Z_(W1)) between the electrode 33 andwafer surface 43 (voltage V_(W1)), impedance 65 (Z_(W2)) between thewafer surface 43 and plasma-sheath interface 66 (voltage V_(W2)) on thewafer, impedance 67 (Z_(W3)) between the plasma and ground, and reachesthe ground. At this time, the plasma space potential between adjacentfocus ring and wafer must be equal. In other words, it is necessary thatthe following condition, V₀−V_(W2)=V₀−V_(F2), must be fulfilled. Thiscan be expressed by the following formula 6 or formula 7.

[Formula 6]

$\begin{matrix}{\frac{Z_{W\; 1} + Z_{W\; 2}}{Z_{W\; 1} + Z_{W\; 2} + Z_{W\; 3}} = \frac{Z_{F\; 1} + Z_{F\; 2}}{Z_{F\; 1} + Z_{F\; 2} + Z_{F\; 3}}} & (6)\end{matrix}$[Formula 7]

$\begin{matrix}{\frac{Z_{W\; 3}}{Z_{W\; 1} + Z_{W\; 2} + Z_{W\; 3}} = \frac{Z_{F\; 3}}{Z_{F\; 1} + Z_{F\; 2} + Z_{F\; 3}}} & (7)\end{matrix}$

In other words, the voltage drop of the RF voltage from electrode 33 toplasma-sheath interface 66 above the wafer must be equal to the voltagedrop of the RF voltage from electrode 33 to plasma-sheath interface 62above the focus ring. The Z_(F1) and V_(W1) mentioned here include theimpedance of dielectric film 34 on the surface of the electrode 33. Itshould be noted that the plasma-sheath interface flattening includesoptimizing the structure and material property of the dielectric film34.

The above-mentioned conditions do not necessarily assure that theplasma-sheath interface above the wafer surface and the plasma-sheathinterface above the focus ring surface are flattened, and anotheradditional condition is required. This is explained with reference tothe marks shown in FIG. 3. The sum of the wafer surface height (H_(w))measured from a certain height reference point 38 and the sheaththickness (d_(w)) above the wafer must equal the sum of the focus ringsurface height (H_(FR)) measured from the same reference point 38 andthe sheath thickness (d_(FR)) above the focus ring. This is expressed bythe following formula 8.

[Formula 8]H _(W) +d _(w) =H _(FR) +d _(FR)  (8)

Through use of the above-mentioned plasma-sheath model, equivalentcircuit analysis and sheath flattening conditions, it is possible todetermine the material and size of the actual structure. Hereafter, wewill describe the contents of the invention based on preferredembodiments.

FIG. 9 illustrates a second embodiment of the present invention, inwhich a wafer 72 and a focus ring 73 are mounted on an electrode 70having a dielectric film 71 for electrostatic chuck. A flatplasma-sheath interface 74 is formed above the wafer 72 and focus ring73. The height of surfaces of the wafer 72 and the focus ring 73 are thesame. In order to fulfill this condition, according to formula 8,H_(W)=H_(FR) and d_(W)=d_(FR). In other words, V₀−V_(W1)=V₀−V_(F1). Fromthese equations, the following formula is obtained.

[Formula 9]

$\begin{matrix}{\frac{Z_{W\; 1}}{Z_{W\; 1} + Z_{W\; 2} + Z_{W\; 3}} = \frac{Z_{F\; 1}}{Z_{F\; 1} + Z_{F\; 2} + Z_{F\; 3}}} & (9)\end{matrix}$

By forming simultaneous equations of formulas 7 and 9, the followingformula 10 is obtained. This is the plasma-sheath interface flatteningcondition of FIG. 9.

[Formula 10]Z_(W1):Z_(W2):Z_(W3)=Z_(F1):Z_(F2):Z_(F3)  (10)

By assigning individual conditions into formulas 7 and 8, theplasma-sheath interface flattening conditions corresponding to thosespecific conditions can be obtained. At this time, a gap (G_(WF)) existsbetween the wafer and focus ring, and there is a precondition that thisgap will not disturb the electric field in the sheath. Therefore, atleast the following equation must be fulfilled, which is0<G_(WF)<d_(W)=d_(FR). As long as these conditions are fulfilled, theelectrode 70, the dielectric film 71 and the focus ring 73 can bedesigned freely. As for materials, the electrode 70 must be a conductivematerial, but the dielectric film 71 can be formed of any material aslong as it is dielectric, and the focus ring 73 can be formed of anymaterial or any combination of materials. The ions being incident on theplasma-sheath interface 74 are accelerated perpendicularly to theplasma-sheath interface 74 and toward the wafer 72.

In order to prevent the generation of defective products caused byparticles adhered on the surface of the wafer, the focus ring isoperated in such a condition as to prevent reaction products generatedby the wafer processing from depositing thereon. This is achieved bysetting the surface voltage of the focus ring to exceed a given value,and to remove the reaction products by ion sputtering. This means thatthe focus ring itself is subjected to ion sputtering. In other words,the focus ring will be consumed and the height thereof will reduce withtime. Here, if a focus ring is used starting from a state in which theplasma-sheath interface 74 is flat, the height of the focus ring 73 willbe reduced along with the increase in operating time, and the processuniformity will be deteriorated at the wafer edge area. In order toextend the life of the focus ring while ensuring process performance,the height of the focus ring must be higher than that of theplasma-sheath interface flattening condition shown in FIG. 9. Thus, asheath height difference d_(of) is defined by the following formula 11,and the relationship between the sheath height difference and the etchrate uniformity at the wafer edge area was sought by experiment.

[Formula 11]d _(of)=(H _(W) +d _(w))−(H _(FR) +d _(FR))  (11)

The result is shown in FIG. 10. FIG. 10 shows the sheath heightdifference on the horizontal axis and plots the etch rate uniformity onthe vertical axis. The definition of etch rate uniformity ER_(of) isshown in FIG. 10. As illustrated, there is a certain correlation betweenthe sheath height difference and etch rate uniformity, and anapproximation straight line can be drawn toward the positive andnegative directions, respectively. If the tolerance of the etch rateuniformity at the wafer edge area is +−3%, the tolerance of the sheathheight difference is approximately +1.5 to −1.0 mm. When the focus ringmaterial is formed of a conductive material, the dimension thereofregarding the tolerance of the sheath height difference can bedetermined by adjusting the thickness of the focus ring. This is becausethe surface voltage of a conductor will not change even when the heightthereof is changed. If the focus ring is made of a dielectric orsemiconductor material, the tolerance of the sheath height differencecan be converted to a tolerance of a focus ring surface voltage throughuse of formula 2, and the necessary impedance and consequently the focusring structure can be computed via equivalent circuit analysis.

Regardless of the material of the focus ring, when a new focus ring isdisposed, the thickness of the focus ring is determined so that theplasma-sheath interface above the focus ring is higher than theplasma-sheath interface above the wafer for a height corresponding tothe tolerance of the sheath height difference, as illustrated in FIG.11( a) showing the third embodiment of the present invention. At thistime, as shown in the circled portion of the drawing, the heightdifference of the plasma-sheath interface acts as a spherical lens fordiverging ions with respect to the wafer. When the height of theplasma-sheath interface above the focus ring is reduced to the lowesttolerance from the plasma-sheath interface above the wafer due toconsumption, the focus ring reaches its application limit, and will haveto be replaced. At this time, as shown in the circled portion of thedrawing, the height difference of the plasma-sheath interface acts as aspherical lens focusing the ions with respect to the wafer. By designingthe focus ring as described, if the tolerance is set as shown in FIG.10, for example, the consumable amount of height of the focus ring isapproximately 2.5 mm. If the focus ring has the most preferable heightfrom the beginning as shown in FIG. 9, the consumable amount of heightof the focus ring is only approximately 1 mm, so by setting thetolerance as mentioned, the life of the focus ring is extended byapproximately 2.5 times. The advantage here is that the suppliesexpenses regarding semiconductor fabrication is reduced as a result.However, the tolerance of a process that determines the basic value ofthe design must be determined to correspond to each process from theviewpoint of securing product performance, so it cannot be designedspecifically in advance for the apparatus. The design of the focus ringmust be determined after determining the mass-production processes.

The wafer surface voltage is an extremely important factor for ensuringthe performance of the process. On the other hand, the focus ringsurface voltage is an important factor for determining the life of thefocus ring or the plasma gas component control related to sputtering ofthe focus ring. Moreover, it also determines whether reaction productscaused during processing is deposited on the focus ring surface or not.FIG. 12 shows the relationship between the focus ring surface voltage(V_(F1)) and focus ring etching rate (ER_(d)) of a quarts focus ringwhen a plasma generated from an Ar/C₅F₈ gas of 2.0 Pa and having anelectron density corresponding to approximately 8×10⁻¹⁶ m⁻³ isgenerated. It is shown here that reaction products are deposited whenthe ER_(d) was of negative value. In this example, the threshold voltageof reaction product deposition was approximately 210 V. Under suchconditions, we will consider a case in which it is preferable to havethe focus ring consumption held down to a minimum while applying asufficiently high RF bias to the wafer. In other words, V_(W1) isgreater than V_(F1) (V_(W1)>V_(F1)) wherein wafer surface voltage isV_(W1) and focus ring surface voltage is V_(F1). At this time, accordingto formula 2 (use V_(W1) or V_(F1) instead of V_(sh)), d_(W) is greaterthan d_(FR) (d_(W)>d_(FR)). Since the wafer and focus ring are separatedby only approximately a few mm, there is no difference in plasmaparameters between them, and the sheath thickness difference is causedby the surface voltage difference. At this time, formula 8 istransformed to obtain formula 12.

[Formula 12]d _(w) −d _(FR) =H _(FR) −H _(W)  (12)

The above formula shows that when the sheath thickness above the waferand the sheath thickness above the focus ring differ, the differencemust be absorbed by adjusting the wafer and focus ring heights. This isthe plasma-sheath interface flattening condition in case whereV_(W1)>V_(F1). FIG. 13 illustrates this condition, which is the fourthembodiment of the present invention. Naturally, the precondition0<G_(WF)<d_(FR)<d_(W) must be fulfilled. Regarding the structure shownin FIG. 13, the height of the focus ring 73 can be redesignedcorresponding to the process variation tolerance described in FIG. 10 inorder to determine the final structure of the focus ring 73.

When V_(W1)=V_(F1), the contents described with reference to FIG. 9 isthe plasma-sheath interface flattening conditions, and FIG. 11 is thefinal structure. Next, we will consider a case where V_(W1)<V_(F1). Thiscorresponds for example to a case where sufficient RF bias is applied tothe focus ring while it is not preferable to apply much RF bias to thewafer when the gas-phase component in the plasma is actively manipulatedthrough vapor phase reaction caused by the surface reaction of the focusring or reaction products caused by the focus ring. Even in this case,formula 12 is effective, and the heights of the wafer and the focus ringmust be adjusted when there is a height difference in the sheaththickness above the wafer and sheath thickness above the focus ring.This is the plasma-sheath interface flattening condition whenV_(W1)<V_(F1). FIG. 14 illustrates this state, which is the fifthembodiment of the present invention. Naturally, the precondition0<G_(WF)<d_(W)<d_(FR) must be fulfilled. Regarding the structure shownin FIG. 14, the height of the focus ring 73 can be redesignedcorresponding to the process variation tolerance described in FIG. 10 inorder to determine the final structure of the focus ring 73.

Now, the sixth embodiment of the present invention is described withreference to FIG. 15. According to this embodiment, a focus ring 76 madeof a conductive material and a wafer 72 are disposed on an electrode 70having a dielectric film 71 for electrostatic chuck. Further, adielectric layer 75 is formed between the focus ring 76 and thedielectric film 71. A flat plasma-sheath interface 74 exists above thewafer 72 and focus ring 76. Therefore, the present embodiment fulfillsthe conditions of formula 7, formula 8 and formula 12, and the designfulfills V_(W1)>V_(F1). Further, the precondition 0<G_(WF)<d_(W)<d_(FR)is also fulfilled. Now, the two-dimensional plasma analysis andtwo-dimensional electric field analysis explained with reference to FIG.7 are carried out, by which the ion sheath and the electric fieldstructure within the dielectric body are analyzed. Here, a firstequi-potential surface 77 of V that fulfills the equationV_(s)=V_(w2)=V_(F2)<V<V_(F1) and a second equi-potential surface 78 of Vthat fulfills the equation V_(W1)>V>V_(F1) are shown as examples of theequi-potential surface. The first equi-potential surface 77 existingabove the wafer 72 and focus ring 76 passes below the plasma-sheathinterface 74, and it has a substantially flat plane. However, the secondequi-potential surface 78 is bent drastically at the edge of the wafer72 and curves in toward the back surface of the wafer. This is becausethe focus ring 76 is made of a conductor and the voltage at variousareas of the focus ring 76 equals V_(F1).

As a result, it was discovered that the second equi-potential surface 78passed through the very narrow gap between the back surface of the wafer72 and the focus ring 76, and further between the focus ring 76 and thedielectric film 71 before entering the dielectric layer 71. As a result,as illustrated in the circled area in FIG. 15, the ions entering thisarea are accelerated perpendicularly toward the wafer until they reachthe first equi-potential surface 77, but when they reach the height nearthe second equi-potential surface 78, they are accelerated also towardthe center of the wafer. In other words, the drawing shows that ionconvergence is performed near the wafer edge by the electric field inthe sheath. Whether or not this ion convergence affects the processuniformity near the wafer edge depends on the process, but it shows thatfurther optimization is necessary, including the electric fieldstructure within the sheath. Naturally, regarding the structure of FIG.15, the height of the focus ring 76 can be redesigned corresponding tothe process variation tolerance described in FIG. 10 in order todetermine the final structure of the focus ring 76.

FIG. 16 illustrating a seventh embodiment of the present invention willnow be described, which is an improvement of the sixth embodiment. Thedifference between this embodiment and the embodiment of FIG. 15 is thatthe shapes of the focus ring 76 and dielectric layer 75 are different.Other than that, both adopt the same design, including the conditions.Now, two dimensional plasma analysis and two dimensional electric fieldanalysis were carried out in a manner similar to the sixth embodiment,by which the electric field structure within the ion sheath and thedielectric body were analyzed. As a result, the first equi-potentialsurface 77 was substantially flat, similar to the sixth embodiment. Thesecond equi-potential surface 78 was found to enter the dielectric layer71 from the edge of the wafer 72. As a result, the ion convergence inthe circled area of FIG. 16 was somewhat improved than that of the sixthembodiment. Naturally, regarding the structure of FIG. 16, the height ofthe focus ring 76 can be redesigned corresponding to the processvariation tolerance described in FIG. 10 in order to determine the finalstructure of the focus ring 76.

FIG. 17 illustrating an eighth embodiment of the present invention willnow be described, which is an improvement of the sixth embodiment. Thedifference between this embodiment and the embodiment of FIG. 15 is thatthe focus ring 80 is formed of a dielectric and that a conductive layer79 is disposed in the present embodiment. Other than that, both adoptthe same design, including the conditions. Now, two dimensional plasmaanalysis and two-dimensional electric field analysis were carried out ina manner similar to the sixth embodiment, by which the electric fieldstructure within the ion sheath and the dielectric body were analyzed.As a result, the first equi-potential surface 77 was substantially flat,similar to the sixth embodiment. The second equi-potential surface 78was found to enter the dielectric focus ring 80 from the edge of thewafer 72. As a result, the bending of the second equi-potential surfaceat the wafer edge was further reduced, and the ion convergence in thecircled area of FIG. 17 was greatly improved than that of the sixthembodiment. Naturally, regarding the structure of FIG. 17, the height ofthe focus ring 80 can be redesigned corresponding to the processvariation tolerance described in FIG. 10 in order to determine the finalstructure of the focus ring 80.

FIG. 18 illustrating a ninth embodiment of the present invention willnow be described, which is an improvement of the seventh and eighthembodiments. The difference between this embodiment and the embodimentof FIG. 16 is that the focus ring 80 is formed of a dielectric and thata conductive layer 79 is disposed in the present embodiment. Other thanthat, both adopt the same design, including the conditions. Now, twodimensional plasma analysis and two dimensional electric field analysiswere carried out in a manner similar to the sixth embodiment, by whichthe electric field structure within the ion sheath and the dielectricmember were analyzed. As a result, the first equi-potential surface 77was substantially flat, similar to the sixth embodiment. The secondequi-potential surface 78 was found to enter the dielectric focus ring80 from the edge of the wafer 72. As a result, the bending of the secondequi-potential surface at the wafer edge was even further flattened thanFIG. 17. Thus, the ion convergence in the circled area of FIG. 18 waseven further improved than those of the seventh and eighth embodiments.Naturally, regarding the structure of FIG. 18, the height of the focusring 80 can be redesigned corresponding to the process variationtolerance described in FIG. 10 in order to determine the final structureof the focus ring 80. Here, it is impossible to completely flatten thesecond equi-potential surface 78. In order for the second equi-potentialsurface to be completely flat, the material of the dielectric focus ringdisposed above the second equi-potential surface shown in FIG. 18 musthave a relative dielectric constant of 1, but it is impossible toacquire a solid dielectric body having such property. The secondequi-potential surface is completely flattened only when the structureof FIG. 9 is adopted and the plasma-sheath interface flatteningconditions related to the structure are fulfilled.

As shown in FIGS. 17 and 18, adopting a dielectric member as the focusring causes another advantageous result. If the focus ring is aconductor, the surface voltage V_(F1) is equal across the whole body.This means that if the height of the focus ring made of a conductor isreduced by 2 mm due to consumption, for example, the plasma-sheathinterface above the focus ring is also lowered by 2 mm. In other words,the amount of consumption of the focus ring is reflected directly in thesheath height difference d_(of). However, if the focus ring is formed ofa dielectric, the reduction of height of the focus ring due toconsumption causes the surface voltage V_(F1) to increase. Thus, thesheath thickness is increased, and the lowering of the plasma-sheathinterface above the focus ring becomes smaller than the lowering ofheight of the focus ring. This phenomenon is more significant when thedielectric material has larger voltage drop in the dielectric body. Inother words, it is more advantageous to use a dielectric having lowrelative dielectric constant.

The above-mentioned example was analyzed via equivalent circuit, and therelationship between the focus ring consumption and the sheath heightdifference d_(of) was examined. The result is shown in FIG. 19. Here,relative dielectric constant e=8 denotes a perfect conductor. It isassumed that the tolerance of the sheath height difference explained inFIG. 10 is 2 mm, for example. In the case of a conductive focus ring,the consumption tolerance of the focus ring is 2 mm. However, in thecase of a dielectric having a relative dielectric constant of e=3, theconsumption tolerance of the focus ring reaches 3.4 mm. The consumptionrate of the focus ring differs according to the material and the appliedprocess, so it depends, but the structure can be further optimized bydesigning the focus ring keeping in mind that it is more advantageousfor the relative dielectric constant to be smaller. It can be recognizedfrom the present drawing that by using a dielectric focus ring having arelative dielectric constant of 10, the consumption tolerance of thefocus ring is increased by approximately 10% compared to using aconductive focus ring. Though 10% may seem like a small amount, the costof the focus ring is a major factor in the cost of consumables relatedto the fabrication of semiconductor products, the reduction thereof cancontribute unfailingly to the improvement of productivity.

FIG. 20 shows a tenth embodiment of the present invention. Thecharacteristic feature of the present embodiment is that a first focusring 81 formed of a dielectric material and a second focus ring 82 areequipped. The material of the second focus ring can be a conductor, asemiconductor or a dielectric. This structure is aimed at setting thesurface voltage of the second focus ring 82 higher (or lower) than thesurface voltage of the first focus ring 81. FIG. 20 shows the state inwhich the voltage is set higher. The designing of this structure iscarried out via the following procedure. First, three routes fortransmitting RF power are considered. The first route 83 passes throughthe wafer 72, which is the same as that described with reference toFIGS. 4 and 8. The second route 84 passes only the first focus ring 81,which is also the same as that described with reference to FIGS. 4 and8, similar to the first route 83. The third route 85 passes through thesecond focus ring 82, which is a new route for power introduced for thefirst time by the present design.

The equivalent circuit corresponding to these three routes isillustrated in FIG. 21. The impedance of all the elements described herecan be determined realistically through calculation or measurement, ashave been mentioned heretofore, and can be subjected to numericalanalysis. At this time, the plasma-sheath interface flattening can berealized if the plasma-sheath interface above the wafer 72 and thatabove the first focus ring 81 are flat, so formulas 7 and 8 can beapplied directly. At this time, sheath height difference occurs to theplasma-sheath interface above the boundary between the first and secondfocus rings 81 and 82, as shown by B in FIG. 20. It is necessary thatthe electric field distortion caused by the sheath height difference Bdoes not influence the electric field at the wafer 72 edge shown by C inFIG. 20. The condition for this is W_(F1)>d_(F2), with the sheaththickness d_(F2) above the second focus ring 82 thicker than the sheaththickness above the first focus ring 81. W_(F1) is the width of thesurface of the first focus ring 81, and the definition thereof is shownin FIG. 20. By keeping this condition, the surface potential of thesecond focus ring 82 and the height thereof (the surface heights of thefirst and second focus rings 81 and 82 are the same in FIG. 20) can bedetermined arbitrarily within the existing range of analyzed solution.Based on the above-mentioned equivalent circuit analysis and theplasma-sheath interface flattening condition, a focus ring can bedesigned that flattens the distortion of electric field near the waferedge and enhances the uniformity of the process. Naturally, the heightof the focus ring 81 can be redesigned corresponding to the processvariation tolerance described in FIG. 10 in order to determine the finalstructure of the focus ring 81.

The present invention carries out the optimization process by optimizingthe design of the focus ring surface potential to prevent wafer processreaction products from being deposited on the focus ring.

The present invention has been described with the plasma etching processof wafer taken as the main example. However, the present invention canbe applied generally to any surface processing and processing apparatususing plasma. These apparatuses and processes include a plasma CVDapparatus and CVD process, a plasma ashing apparatus and ashing process,and plasma sputtering apparatus and sputtering process. The presentinvention can also be applied regardless of the plasma generating meansbeing used. The possible plasma generating means include an inductivecoupled plasma generating apparatus, a capacitive coupled plasmagenerating apparatus, an electron cyclotron resonance plasma generatingapparatus, a helicon plasma generating apparatus, a surface wave plasmagenerating apparatus, and a magnetron plasma generating apparatus.Further, the substrate to be processed can include a semiconductorwafer, a dielectric wafer such as a quartz wafer, an LCD substrate and aconductive wafer such as AlTiC.

1. A plasma processing apparatus for processing an object to beprocessed using plasma, the apparatus comprising: a process stage forplacing the object to be processed; a focus ring disposed on the processstage surrounding the object to be processed, the focus ring and theobject to be processed being subjected to application of RF bias; andmeans for performing an equivalent circuit analysis and acquiring both avoltage on the surface of the object to be processed and the focus ring,and a sheath height on the surface of the object to be processed and thefocus ring, wherein the means for performing an equivalent circuitanalysis includes an equivalent circuit modeling of plasma and ionsheath based on a plasma sheath model, simultaneous analysis of a plasmaload on the object to be processed in the ion sheath based on the plasmasheath model and a plasma load on the focus ring, and setting of thecapacitance between the focus ring and the process stage to a valueflattening an equi-potential surface within the ion sheath.
 2. Theplasma processing apparatus according to claim 1, wherein the means forperforming an equivalent circuit analysis includes setting a focus ringsurface height, a focus ring surface voltage, a focus ring material anda focus ring structure so that a height of an ion sheath formed on thefocus ring surface is either equal or has a height difference within anappropriate tolerance range to a height of an ion sheath formed on thewafer surface.
 3. The plasma processing apparatus according to claim 1,wherein the means for performing an equivalent circuit analysis includessetting the structure based on an appropriate tolerance taking intoconsideration a variation by time caused by consumption of the focusring.
 4. The plasma processing apparatus according to claim 1, whereinthe means for performing an equivalent circuit analysis includes twodimensional plasma analysis and two dimensional electric field analysis.5. The plasma processing apparatus according to claim 1, wherein themeans for performing an equivalent circuit analysis includes twoplasma-sheath interface flattening conditions, one of which is that avoltage drop of an RF voltage from an electrode in the process stage tothe plasma-sheath interface above the object to be processed is set tobe equal to the voltage drop of the RF voltage from the electrode in theprocessing stage to the plasma-sheath interface above the focus ring. 6.The plasma processing apparatus according to claim 1, wherein the meansfor performing an equivalent circuit analysis includes two plasma-sheathinterface flattening conditions, one of which is that a sum of a surfaceheight of the object to be processed measured from a certain heightreference point and a sheath thickness above the object to be processedis set to be equal to a sum of a surface height of the focus ringmeasured from the height reference point and the sheath thickness abovethe focus ring.